Question

tell whether each linear function is a direct variation. if so, identify the constant of variation.

1. ( 2x - 6y = 0 )
2. ( x - y = 8 )
3. ( 4x = -6y )
4. the value of ( y ) varies directly with ( x ), and ( y = 4 ) when ( x = -12 ). find ( y ) when ( x = -27 ).
5. yoga fun charges a $63 starting fee plus $112 per class. yoga for all charges no starting fee and $15 per class. for how many classes will the cost be the same at both places?

a. 3 classes
b. 5 classes
c. 21 classes
d. 27 classes

Explanation:

Step1: Define Cost Functions

Let \( n \) be the number of classes.
Cost for Yoga Fun: \( C_1 = 63 + 12n \) (starting fee + per - class cost).
Cost for Yoga For All: \( C_2 = 15n \) (no starting fee, per - class cost).

Step2: Set Costs Equal

To find when costs are the same, set \( C_1 = C_2 \):
\( 63 + 12n = 15n \)

Step3: Solve for \( n \)

Subtract \( 12n \) from both sides:
\( 63 = 15n - 12n \)
\( 63 = 3n \)

Divide both sides by 3:
\( n=\frac{63}{3}=21 \)

Answer:

C. 21 classes